A1 Refereed original research article in a scientific journal
Robustifying principal component analysis with spatial sign vectors
Authors: Taskinen S, Koch I, Oja H
Publisher: ELSEVIER SCIENCE BV
Publication year: 2012
Journal: Statistics and Probability Letters
Journal name in source: STATISTICS & PROBABILITY LETTERS
Journal acronym: STAT PROBABIL LETT
Volume: 82
Issue: 4
First page : 765
Last page: 774
Number of pages: 10
ISSN: 0167-7152
DOI: https://doi.org/10.1016/j.spl.2012.01.001
Abstract
In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods. (C) 2012 Elsevier B.V. All rights reserved.
In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods. (C) 2012 Elsevier B.V. All rights reserved.
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